# A cylindrical can is to be made to hold 1000cm^3 of oil. How do you find the dimensions that will minimize the cost of metal to manufacture the can?

Height = 10.84 cm, radius of the base = 5.42 cm and material for the surface =37 square cm, nearly

Let height = h and radius of the base = r.

and surface area of the can

Correspondingly, h= 10.84 cm, nearly

There is no maximum for S. Also,

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To minimize the cost of metal to manufacture the cylindrical can holding 1000 cm^3 of oil, you would need to find the dimensions that minimize the surface area of the can. The formula for the surface area of a cylinder is given by A = 2πrh + πr^2, where r is the radius and h is the height. Using the volume formula V = πr^2h, you can express the height h in terms of the volume V and the radius r. Then, substitute this expression for h into the formula for surface area A. Finally, differentiate the resulting expression for A with respect to r, set it equal to zero, and solve for r to find the radius that minimizes the surface area, hence minimizing the cost of metal.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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